The aim of this protocol is to determine the antihemostatic dose-response effects of HIRULOG(TM) in renal failure patients treated with chronic hemodialysis by administering the drug according to a dose escalating regimen while measuring platelet and coagulation hemostatic functions. This study will document a safe and effective regimen for use in testing the hypothesis that this direct antithrombin peptide prevents failure of arteriovenous vascular access grafts in dialysis patients. Twelve subjects have been studied, and three more are being recruited.